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Factor completely: 16x^(2)(x^(2)-5)-9(x^(2)-5) Answer:

Factor completely:\newline16x2(x2−5)−9(x2−5) 16 x^{2}\left(x^{2}-5\right)-9\left(x^{2}-5\right) \newlineAnswer:

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Full solution

Q. Factor completely:\newline16x2(x2−5)−9(x2−5) 16 x^{2}\left(x^{2}-5\right)-9\left(x^{2}-5\right) \newlineAnswer:
  1. Identify common factor: Identify the common factor in both terms.\newlineThe common factor in both terms is (x2−5)(x^{2} - 5).
  2. Factor out common factor: Factor out the common factor from both terms.\newlineThe expression can be written as (x2−5)(16x2−9)(x^{2} - 5)(16x^{2} - 9).
  3. Recognize perfect squares: Recognize that both terms in the parentheses are perfect squares. 16x216x^{2} is the square of 4x4x, and 99 is the square of 33.
  4. Factor difference of squares: Factor the difference of squares in the second term.\newlineThe expression (16x2−9)(16x^{2} - 9) can be factored as (4x+3)(4x−3)(4x + 3)(4x - 3).
  5. Write final factored form: Write the final factored form of the original expression.\newlineThe completely factored form is (x2−5)(4x+3)(4x−3)(x^{2} - 5)(4x + 3)(4x - 3).

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